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The oblateness and mass variation effects are studied in the circular Hill restricted 4-body problem (R4BP). Here we assume two bodies as oblate in shape and third one as spherical in shape, these three bodies are at the vertices of a triangle. The 4th infinitesimal body varies its mass and moving under the perturbed gravitational forces in the plane of primaries. With these perturbations, we evaluate the equations of motion and quasi-jacobian integral using specific scales and transformations. Finally, the numerical presentations are given such as stationary points, regions of motion, surfaces of section, periodic orbits and basins of convergence. 2010 MSC: 00-01, 99-00

In this study, the modified Green and Lindsay model is utilized to discuss the effects of heating caused by surface absorption of laser radiation in a two-dimensional thermoelastic half-space. The temporal profile of the pulsed laser is taken as a non-Gaussian and the spatial one is a Gaussian. The medium surface is taken to be traction free. The integral transform method is utilized to obtain the general solution by applying the two transformations Hankel and Laplace, in which the inverse of Laplace is performed numerically. The Silicon material is considered as an example to verify the consistency of the obtained results of the new model.

The prime objective of the current study is to examine the effects of third-grade hybrid nanofluid with natural convection utilizing the ferro-particle Fe 3 O 4 and titanium dioxide TiO 2 and sodium alginate (SA) as a host fluid, flowing through vertical parallel plates, under the fuzzy atmosphere. The dimensionless highly nonlinear coupled ordinary differential equations are computed adopting the bvp4c numerical approach. This is an extremely effective technique with a low computational cost. For validation, it is found that as the volume fraction of Fe 3 O 4 + TiO 2 hybrid nanoparticles rises, so does the heat transfer rate. The current and existing results with their comparisons are shown in the form of the tables. The present findings are in good agreement with their previous numerical and analytical results in a crisp atmosphere. The nanoparticles volume fraction of Fe 3 O 4 and TiO 2 is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs) [0, 0.05, 0.1]. The TFNs are controlled by α − cut and the variability of the uncertainty is studied through triangular membership function (MF).

The oblateness and mass variation effects are studied in the circular Hill restricted 4-body problem (R4BP). Here we assume two bodies as oblate in shape and third one as spherical in shape, these three bodies are at the vertices of a triangle. The 4th infinitesimal body varies its mass and moving under the perturbed gravitational forces in the plane of primaries. With these perturbations, we evaluate the equations of motion and quasi-jacobian integral using specific scales and transformations. Finally, the numerical presentations are given such as stationary points, regions of motion, surfaces of section, periodic orbits and basins of convergence.

In this paper, we present new results on deterministic sudden changes and stochastic fluctuations’ effects on the dynamics of a two-predator one-prey model. We purpose to study the dynamics of the model with some impacting factors as the problem statement. The methodology depends on investigating the seasonality and stochastic terms which make the predator-prey interactions more realistic. A theoretical analysis is introduced for studying the effects of sudden deterministic changes, using three different cases of sudden changes. We show that the system in a good situation presents persistence dynamics only as a stable dynamical behavior. However, the system in a bad situation leads to three main outcomes as follows: first, constancy at the initial conditions of the prey and predators; second, extinction of the whole system; third, extinction of both predators, resulting in the growth of the prey population until it reaches a peak carrying capacity. We perform numerical simulations to study effects of stochastic fluctuations, which show that noise strength leads to an increase in the oscillations in the dynamical behavior and became more complex and finally leads to extinction when the strength of the noise is high. The random noises transfer the dynamical behavior from the equilibrium case to the oscillation case, which describes some unstable environments.

An exact solution of the problem regarding influence of chemical reaction and buoyant force on the heat and mass transfer in a radiative flow due to non-coaxial rotation of a disk and fluid at infinity is derived by using Laplace transform. Flow fields are displayed for various values of dimensionless parameters. Shear stresses at the surface of disk and shear stresses at the disk for very large time are calculated. The effects of Grashof number and Hartmann number on the steady state shear stresses at the disk are noted and presented.

Thermal relaxation phenomenon and generalized heat flux theory accurately determine the heat transfer for characteristics in industrial fluid like polymers. The rheology of polymers is best characterized by vortex and spin gradient viscosities and couple stresses. This article models the impact of hybridity of nano-structures on thermal performance of the micropolar fluid using novel heat flux theory. Mathematical models are used is analyze the behavior of temperature wall heat flux. Noslip hydrodynamic boundary conditions are implemented in order to examine the thermal performance of micropolar fluid. Numerical simulations are carried out via finite element method (FEM). A remarkable impact of hybridity of nano-structures on transport of heat is noted. Dissipation of heat has played a vital role in enhancing the thermal boundary layer thickness. The heat dissipated in hybrid nanofluid is greater than heat dissipation of heat in mono-nanofluid. Temperature of both mono and hybrid nanofluid has shown a decreasing trend when Deborah number is increased. This is due to the fact that fluid restores its original thermal state and resists against thermal change in its state. Heat flux has shown increasing trend versus change in magnetic field intensity. Further, heat flux has shown increasing trend versus an increase in vortex viscosity parameter.

This study explores the heat and mass transfer of Casson nanofluid flow containing gyrotactic microorganisms past a swirling cylinder. Fluid flow is generated owing to the torsional movement of the cylinder. An analysis is performed in the presence of gyrotactic microorganisms. The effects of chemical reaction, magnetohydrodynamics, heat generation/absorption, and zero mass flux condition are also considered. The Cattaneo–Christov heat flux model is initiated instead of conventional Fourier heat flux. Apposite transformations are betrothed to attain the coupled system of equations. The numerical solution is developed from the novel mathematical model via bvp4c function utilizing MATLAB software. Numerous graphs and tables are established to portray the inspiration of embroiled parameters on the flow distributions. To corroborate the presented results; a comparison to an already done published paper is also made. An excellent synchronization between the two results is obtained thus endorsing the presented model. Also, form the graphical structures and numerically erected tables, it is professed that concentration of the fluid is lessened owing to an upsurge in values of Reynolds number and Brownian motion parameter. Furthermore, diminishing density of microorganism is perceived for mounting estimates of bioconvection Peclet number.

In this article we use a non-classical approach to investigate different physical effects of Cosserat-Maxwell fluid flow with non-Fourier heat transfer mechanism. Furthermore, a new numerical approach is used and outlined for computing and analyzing the behavior of such flows. In particular, continuous Galerkin-Petrov discretization scheme is embedded with shooting method to get the numerical algorithm to solve the stagnation point flow of Cosserat-Maxwell fluid with Cattaneo-Christov heat transfer. The mathematical description of the physical problem is stated in the form of partial differential equations (PDEs) which govern the flow mechanism. Further, the suitable transformations are utilized to describe the governing PDEs into their respective ordinary differential equations. Numerical experiments are performed for a specific case where there are weak concentrations of the flow near the stretching surface thereby allowing the microelement to rotate and generate vortex flow near the stretching surface. Buoyancy effects along with other interesting physical effects are calculated and numerical results are presented for various fluidic situations. Several benchmark case studies were carried out for the validation of obtained results. Moreover, the results are also validated against the results available in the limiting classical continuum case in literature and a good agreement is found.

Fourier law of heat conduction, its analog Fick's first law, and Newton's law of viscosity are classical laws that are not capable of exhibiting memory effects. Conservation laws based on these classical laws do not give predictions about memory effects on the transport phenomena. Recently, proposed novel laws are called Cattaneo–Christov heat flux. Models are based on the generalization of classical laws of heat conduction, mass diffusion, and Newton's law of viscosity. This investigation considers this generalized theory to model the impact of relaxation phenomenon on the transport of momentum, heat, and mass in Maxwell fluid (viscoelastic fluid) of temperature-dependent viscosity and thermal conductivity in the presence of temperature-dependent mass diffusion coefficients. It is observed from the simulations that memory effects play a key role in controlling momentum, thermal and concentration boundary layer thicknesses. It is also noted that the rate of diffusion of heat and mass has shown an increasing trend when thermal conductivity and mass diffusion coefficients are increased via rise in temperature of the fluid. The generative chemical reaction on the transport of specie relative to the impact on the transport of specie when it is compared with the impact of destructive chemical reaction on the transport of specie.

The electrodynamic instability of a self-gravitating liquid jet (radius R) of density ambient with a finite liquid (radius qR with ) of density has been developed. The problem is formulated and upon The electric field is strongly stabilizing as (the dielectric constant). The gravitational force is destabilizing only for small axisymmetric perturbed wave length. The densities ratio and radii ratio q play important roles in stabilizing the compound liquid jet. It is found that whatever are the strong effects of the stabilizing different factors, the gravitational destabilizing character of the model will never be suppressed.

Transport phenomenon is central for understanding many procedures in numerous sciences, transport phenomena can be described by the partial differential equation. Forward Time Centered Space scheme give ample numerical solutions of the transport equation. In this paper, we apply Forward Time Centered Space scheme to solve a non-trivial transport problem using different step sizes of time (t) and space (x). We use MATLAB software to get the numerical results. The numerical simulation presents that the FTCS scheme is more stable and closer to the exact solution when we decrease step sizes of t, x and more and more.

Double diffusion models with Carreau rheology strain-relations and correlations for thermal physical properties are used to model double diffusion phenomenon in Carreau liquid passing a wedge-shaped body. Normalized conservation equations are solved numerically using finite element method (FEM). Linear shaped functions are used in weak forms of models under Galerikin approximations. Convergence and mesh free analysis are performed and results are validated. The numerical simulations against parametric analysis are also observed. Suspension of hybrid nano-structures has significantly increased the effectiveness of thermal conductivity and an enhance in thermal and mass transport is observed. An increase in thermal radiations causes a remarkable decrease in temperature. Weissenberg parameter decreases velocity of Carreau liquid in the presence of magnetic field and hybrid nano-structures. The chemical reaction has an impact on the diffusion of specie from wedge into fluid increases for the case of generative chemical reaction whereas opposite trend is noted in case of destructive chemical reaction.

Computational fluid dynamics (CFD) tools are applied to model transportation activity in micropolar fluid suspension with density particles and mono and hybrid metallic nano-sized structures. Highly complex computational models obtained by CFD simulations are executed via the finite element method. Galerkin residuals are approximated by Galerkin approximations. The assembled nonlinear system is linearized and solved iteratively under reasonable computational tolerance. A notable impact of vortex viscosity is observed during transportation of macro- and micro-momentum. The velocity of dust particles has been predicted via the variation of dust particle interaction parameter. Angular velocity for both mono and hybrid nanofluids is found to increase as a function of vortex viscosity. Furthermore, it is noted that the micro-rotation field associated with mono–nanofluid has a higher value than the micro-rotation field associated with hybrid nanofluids.

Various ecological models have contributed much to gaining a better understanding of prey–predator interactions. In this paper, an extension of the basic model involving two predators competing on one prey is introduced. The equilibrium points and stability of the points are discussed. The existence of limit cycle and consequent complex dynamical behaviors are shown through a new procedure recently introduced. The persistence and extinction of predators are presented in different forms as steady state, limit cycle, and complex dynamical behaviors.

A model of two competing predators sharing one prey is introduced. In the model, the seasonality in the functional response is investigated. Kolmogorov’s conditions are obtained to validate the values of the parameters. In the numerical simulations, we show the effects of the seasonality strength on the persistence and extinction of predators, the results are supported through the mathematical analysis.

A prey predator model with Crowley — Martin functional response is introduced. In the model, seasonality in the functional response which determined the search and capture's parameters is investigated and Kolmogorov's analysis is applied to validate the values of the parameters. From the numerical simulations presented through Time series and Phase space figures, complex dynamics were observed.